Carbon nanotubes possess many interesting properties, which make them a promising material for a variety of applications. In this paper, we present a unified framework for the simulation of the mechanical behavior of carbon nanotubes. It allows the creation, simulation and visualization of these structures, extending previous work by the research group “MISMO” at TU Darmstadt. In particular, we develop and integrate a new matrix-free iterative solving procedure, employing the conjugate gradient method, that drastically reduces the memory consumption in comparison to the existing approaches. The increase in operations for the memory saving approach is partially offset by a well scaling shared-memory parallelization. In addition the hotspots in the code have been vectorized. Altogether, the resulting simulation framework enables the simulation of complex carbon nanotubes on commodity multicore desktop computers.